Spatially varying auto‐regressive models for prediction of new human immunodeficiency virus diagnoses

In demand of predicting new human immunodeficiency virus (HIV) diagnosis rates based on publicly available HIV data that are abundant in space but have few points in time, we propose a class of spatially varying auto‐regressive models compounded with conditional auto‐regressive spatial correlation structures. We then propose to use the copula approach and a flexible conditional auto‐regressive formulation to model the dependence between adjacent counties. These models allow for spatial and temporal correlation as well as space–time interactions and are naturally suitable for predicting HIV cases and other spatiotemporal disease data that feature a similar data structure. We apply the proposed models to HIV data over Florida, California and New England states and compare them with a range of linear mixed models that have been recently popular for modelling spatiotemporal disease data. The results show that for such data our proposed models outperform the others in terms of prediction.